Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. CT systems generally create images of one or more sectional slices through a subject's body. A radiation source, such as an X-ray source, irradiates the body from one side. At least one detector on the opposite side of the body receives radiation transmitted through the body. The attenuation of the radiation that has passed through the body is measured by processing electrical signals received from the detector.
A CT sinogram indicates attenuation through the body as a function of position along a detector array and as a function of the projection angle from the X-ray source to an X-ray detector. In a sinogram, the spatial dimensions refer to the position along the array of X-ray detectors. The time/angle dimension refers to the projection angle of X-rays, which changes as a function of time during a CT scan. The attenuation resulting from a portion of the imaged object will trace out a sine wave along the axis corresponding to the projection angle. Those portions farther from the axis of rotation correspond to sine waves with larger amplitudes, and the phase of the sine waves correspond to the angular positions around the rotation axis. Performing an inverse Radon transform—or any other image reconstruction method—reconstructs an image from the projection data represented in the sinogram.
Statistical iterative reconstruction (IR) algorithms in tomography can provide improved image quality at reduced dose levels relative to more conventional reconstruction methods like filtered back-projection (FBP). However, in certain implementations, the statistical approach is slow, requiring substantial computation time. To remedy the slow computationally intensive operation of standard statistical reconstruction approaches, improved methods using iterative algorithms for statistical reconstruction that converge more quickly in fewer iterations are gaining recognition.
Accelerator methods can be variously combined with IR methods, including ordered subsets (OS), and Nesterov's acceleration techniques. OS methods beneficially reduce the computational cost by using only a subset of the measurement data per iteration of the image reconstruction algorithm. Nesterov's acceleration method can also be used to improve computational efficiency and performance of the IR method. However, as described below for certain implementations, OS accelerated algorithms might not converge. For example, when combined with the Nesterov's acceleration, OS accelerated algorithms can suffer from divergence issues.